Equivalent Frame

1098 • Appendix A Design Aids

TABLE A-13 Lap-Splice Lengths for Grade-60 Bars in Columns (in.)

Bar No.

(psi) 5 6 7 8 9 10 11

Compression lap splices

Lap splice

26 31 35 40 46 51 5619 23 26 30 34 38 42

Tension lap splices

Lap splice

Class A tension lap splice: half or fewer of the bars spliced at any location and in tension (ACI Code Section 12.17.2.2)

3000 27.4 32.9 48.0 54.8 61.8 69.6 77.34000 23.7 28.4 41.5 47.4 53.5 60.2 66.85000 21.2 25.4 37.1 42.4 47.8 53.8 59.86000 19.4 23.3 33.9 38.7 43.7 49.1 54.6

Class B tension lap splices: more than half of the bars spliced at any section and/or greater than in tension (ACI Code Section 12.17.2.2)

3000 35.6 42.7 62.3 71.2 80.4 90.5 1004000 30.8 37.0 53.9 61.6 69.5 78.3 86.95000 27.5 33.0 48.2 55.1 62.1 70.0 77.76000 25.2 30.2 44.0 50.3 56.7 63.9 70.9

aCompression lap splices may be multiplied by 0.83 or 0.75 if enclosed by ties orspirals satisfying ACI Code Sections 12.17.2.4 or 12.17.2.5.b factor, factor.l = lightweight - concretece = coating

0.5fyfs

0 … fs … 0.5fy

length = 1length from table2 * ce >l (noteb)

Ú300063000

length = 1length from table2 * 1factors in notea2

fcœ

TABLE A-14 Moment-Distribution Factors for Slabs without Drop Panelsa

Carryover factor � COF

0.00 0.05 0.10 0.15 0.20 0.25

0.00 M 0.083 0.083 0.083 0.083 0.083 0.083k 4.000 4.000 4.000 4.000 4.000 4.000COF 0.500 0.500 0.500 0.500 0.500 0.500

0.05 M 0.083 0.084 0.084 0.084 0.085 0.085k 4.000 4.047 4.093 4.138 4.181 4.222COF 0.500 0.503 0.507 0.510 0.513 0.516

0.10 M 0.083 0.084 0.085 0.085 0.086 0.087k 4.000 4.091 4.182 4.272 4.362 4.449COF 0.500 0.506 0.513 0.519 0.524 0.530

0.15 M 0.083 0.084 0.085 0.086 0.087 0.088k 4.000 4.132 4.267 4.403 4.541 4.680COF 0.500 0.509 0.517 0.526 0.534 0.543

0.20 M 0.083 0.085 0.086 0.087 0.088 0.089k 4.000 4.170 4.346 4.529 4.717 4.910COF 0.500 0.511 0.522 0.532 0.543 0.554

0.25 M 0.083 0.085 0.086 0.087 0.089 0.090k 4.000 4.204 4.420 4.648 4.887 5.138COF 0.500 0.512 0.525 0.538 0.550 0.563

1.000 0.856 0.729 0.613 0.512 0.421

a and are the widths of the column measured parallel to and Source: [13-16].

/2/1c2c1

x = 11 - c2>/232

c1�/1

c2�/2

K (stiffness) = kE/2t3�12/1FEM (uniform load w) = Mw/2/1

2

Can be usedfor slabs withbeams

Appendix A Design Aids • 1099

TABLE A-15 Moment-Distribution Factors for Slabs with Drop Panels; h1 � 1.5ha


0.00 0.05 0.10 0.15 0.20 0.25 0.30

0.00 M 0.088 0.088 0.088 0.088 0.088 0.088 0.088k 4.795 4.795 4.795 4.795 4.795 4.795 4.795COF 0.542 0.542 0.542 0.542 0.542 0.542 0.542

0.05 M 0.088 0.088 0.089 0.089 0.089 0.089 0.090k 4.795 4.846 4.896 4.944 4.990 5.035 5.077COF 0.542 0.545 0.548 0.551 0.553 0.556 0.558

0.10 M 0.088 0.088 0.089 0.090 0.090 0.091 0.091k 4.795 4.894 4.992 5.039 5.184 5.278 5.368COF 0.542 0.548 0.553 0.559 0.564 0.569 0.573

0.15 M 0.088 0.089 0.090 0.090 0.091 0.092 0.092k 4.795 4.938 5.082 5.228 5.374 5.520 5.665COF 0.542 0.550 0.558 0.565 0.573 0.580 0.587

0.20 M 0.088 0.089 0.090 0.091 0.092 0.093 0.094k 4.795 4.978 5.167 5.361 5.558 5.760 5.962COF 0.542 0.552 0.562 0.571 0.581 0.590 0.600

0.25 M 0.088 0.089 0.090 0.091 0.092 0.094 0.095k 4.795 5.015 5.245 5.485 5.735 5.994 6.261COF 0.542 0.553 0.565 0.576 0.587 0.598 0.609

0.30 M 0.088 0.089 0.090 0.092 0.093 0.094 0.095k 4.795 5.048 5.317 5.601 5.902 6.219 6.550COF 0.542 0.554 0.567 0.580 0.593 0.605 0.618

ah, Slab thickness; h1, total thickness in drop panel.

Source: [13-16].

c1�/1

c2�/2


2

TABLE A-16 Moment-Distribution Factors for Slabs with Drop Panels; h1 � 1.5ha


0.00 0.05 0.10 0.15 0.20 0.25

0.00 M 0.093 0.093 0.093 0.093 0.093 0.093k 5.837 5.837 5.837 5.837 5.837 5.837COF 0.589 0.589 0.589 0.589 0.589 0.589

0.05 M 0.093 0.093 0.093 0.093 0.094 0.094k 5.837 5.890 5.942 5.993 6.041 6.087COF 0.589 0.591 0.594 0.596 0.598 0.600

0.10 M 0.093 0.093 0.094 0.094 0.094 0.095k 5.837 5.940 6.024 6.142 6.240 6.335COF 0.589 0.593 0.598 0.602 0.607 0.611

0.15 M 0.093 0.093 0.094 0.095 0.095 0.096k 5.837 5.986 6.135 6.284 6.432 6.579COF 0.589 0.595 0.602 0.608 0.614 0.620

0.20 M 0.093 0.093 0.094 0.095 0.096 0.096k 5.837 6.027 6.221 6.418 6.616 6.816COF 0.589 0.597 0.605 0.613 0.621 0.628

0.25 M 0.093 0.094 0.094 0.095 0.096 0.097k 5.837 6.065 6.300 6.543 6.790 7.043COF 0.589 0.598 0.608 0.617 0.626 0.635

ah, Slab thickness; h1, total thickness in drop panel.Source: [13-16].

c1�/1

c2�/2


2

1100 • Appendix A Design Aids

TABLE A-17 Stiffness and Carryover Factors for Columns

1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45

0.00 4.20 4.40 4.60 4.80 5.00 5.20 5.40 5.60 5.800.57 0.65 0.73 0.80 0.87 0.95 1.03 1.10 1.17

0.2 4.31 4.62 4.95 5.30 5.65 6.02 6.40 6.79 7.200.56 0.62 0.68 0.74 0.80 0.85 0.91 0.96 1.01

0.4 4.38 4.79 5.22 5.67 6.15 6.65 7.18 7.74 8.320.55 0.60 0.65 0.70 0.74 0.79 0.83 0.87 0.91

0.6 4.44 4.91 5.42 5.96 6.54 7.15 7.81 8.50 9.230.55 0.59 0.63 0.67 0.70 0.74 0.77 0.80 0.83

0.8 4.49 5.01 5.58 6.19 6.85 7.56 8.31 9.12 9.980.54 0.58 0.61 0.64 0.67 0.70 0.72 0.75 0.77

1.0 4.52 5.09 5.71 6.38 7.11 7.89 8.73 9.63 10.600.54 0.57 0.60 0.62 0.65 0.67 0.69 0.71 0.73

1.2 4.55 5.16 5.82 6.54 7.32 8.17 9.08 10.07 11.120.53 0.56 0.59 0.61 0.63 0.65 0.66 0.68 0.69

1.4 4.58 5.21 5.91 6.68 7.51 8.41 9.38 10.43 11.570.53 0.55 0.58 0.60 0.61 0.63 0.64 0.65 0.66

1.6 4.60 5.26 5.99 6.79 7.66 8.61 9.64 10.75 11.950.53 0.55 0.57 0.59 0.60 0.61 0.62 0.63 0.64

1.8 4.62 5.30 6.06 6.89 7.80 8.79 9.87 11.03 12.290.52 0.55 0.56 0.58 0.59 0.60 0.61 0.61 0.62

2.0 4.63 5.34 6.12 6.98 7.92 8.94 10.06 11.27 12.590.52 0.54 0.56 0.57 0.58 0.59 0.59 0.60 0.60

2.2 4.65 5.37 6.17 7.05 8.02 9.08 10.24 11.49 12.850.52 0.54 0.55 0.56 0.57 0.58 0.58 0.59 0.59

2.4 4.66 5.40 6.22 7.12 8.11 9.20 10.39 11.68 13.080.52 0.53 0.55 0.56 0.56 0.57 0.57 0.58 0.58

2.6 4.67 5.42 6.26 7.18 8.20 9.31 10.53 11.86 13.290.52 0.53 0.54 0.55 0.56 0.56 0.56 0.57 0.57

2.8 4.68 5.44 6.29 7.23 8.27 9.41 10.66 12.01 13.480.52 0.53 0.54 0.55 0.55 0.55 0.56 0.56 0.56

3.0 4.69 5.46 6.33 7.28 8.34 9.50 10.77 12.15 13.650.52 0.53 0.54 0.54 0.55 0.55 0.55 0.55 0.55

3.5 4.71 5.50 6.40 7.39 8.48 9.69 11.01 12.46 14.020.51 0.52 0.53 0.53 0.54 0.54 0.54 0.53 0.53

4.0 4.72 5.54 6.45 7.47 8.60 9.84 11.21 12.70 14.320.51 0.52 0.52 0.53 0.53 0.52 0.52 0.52 0.52

4.5 4.73 5.56 6.50 7.54 8.69 9.97 11.37 12.89 14.570.51 0.52 0.52 0.52 0.52 0.52 0.51 0.51 0.51

5.0 4.75 5.59 6.54 7.60 8.78 10.07 11.50 13.07 14.770.51 0.51 0.52 0.52 0.51 0.51 0.51 0.50 0.49

6.0 4.76 5.63 6.60 7.69 8.90 10.24 11.72 13.33 15.100.51 0.51 0.51 0.51 0.50 0.50 0.49 0.49 0.48

7.0 4.78 5.66 6.65 7.76 9.00 10.37 11.88 13.54 15.340.51 0.51 0.51 0.50 0.50 0.49 0.48 0.48 0.47

8.0 4.78 5.68 6.69 7.82 9.07 10.47 12.01 13.70 15.540.51 0.51 0.50 0.50 0.49 0.49 0.48 0.47 0.46

9.0 4.80 5.71 6.74 7.89 9.18 10.61 12.19 13.93 15.830.50 0.50 0.50 0.49 0.48 0.48 0.47 0.46 0.45

Source: [13-15], courtesy of the Portland Cement Association.

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ta>tb

/c>/u

Kc = kELc/c

A

B

A

B

A

z z

B

Equivalent Frame

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